The 33-year-old, who previously played for Manchester United and Arsenal, could not agree a contract extension at Roma.
Inter did not provide details of Mkhitaryan's contract but he has reportedly signed signed a two-year deal.
Mkhitaryan's arrival followed those of Cameroon goalkeeper Andre Onana, Belgium striker Romelu Lukaku on a season-long loan from Chelsea and Albania midfielder Kristjan Asllani from Empoli.
Inter have also been linked with a move for Juventus forward Paulo Dybala.
